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Simplifying x2 + x + 1 = 0.99 Reorder the terms: 1 + x + x2 = 0.99 Solving 1 + x + x2 = 0.99 Solving for variable 'x'. Reorder the terms: 1 + -0.99 + x + x2 = 0.99 + -0.99 Combine like terms: 1 + -0.99 = 0.01 0.01 + x + x2 = 0.99 + -0.99 Combine like terms: 0.99 + -0.99 = 0.00 0.01 + x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-0.01' to each side of the equation. 0.01 + x + -0.01 + x2 = 0.00 + -0.01 Reorder the terms: 0.01 + -0.01 + x + x2 = 0.00 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x + x2 = 0.00 + -0.01 x + x2 = 0.00 + -0.01 Combine like terms: 0.00 + -0.01 = -0.01 x + x2 = -0.01 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = -0.01 + 0.25 Reorder the terms: 0.25 + x + x2 = -0.01 + 0.25 Combine like terms: -0.01 + 0.25 = 0.24 0.25 + x + x2 = 0.24 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x + 0.5) equal to 0.489897949 and -0.489897949.Subproblem 1
x + 0.5 = 0.489897949 Simplifying x + 0.5 = 0.489897949 Reorder the terms: 0.5 + x = 0.489897949 Solving 0.5 + x = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.489897949 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.489897949 + -0.5 x = 0.489897949 + -0.5 Combine like terms: 0.489897949 + -0.5 = -0.010102051 x = -0.010102051 Simplifying x = -0.010102051Subproblem 2
x + 0.5 = -0.489897949 Simplifying x + 0.5 = -0.489897949 Reorder the terms: 0.5 + x = -0.489897949 Solving 0.5 + x = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.489897949 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.489897949 + -0.5 x = -0.489897949 + -0.5 Combine like terms: -0.489897949 + -0.5 = -0.989897949 x = -0.989897949 Simplifying x = -0.989897949Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.010102051, -0.989897949}
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